A generalization of Frieman's 3k-3 theorem

Abstract

We prove a generalization of Frieman's $3k-3$ theorem for the sumset $${\Sigma }^l(A_1,\dots ,A_k)=\{a_{j_1}+\cdots +a_{j_l}:1\le j_1<\cdots <j_l\le k,a_{j_s}\in A_{j_s}\text{ for all }s\}.$$

arXiv commentSeemingly the main result of this paper is not strong in most cases